February 07, 2006

Hartle on Quantum Spacetime

James B. Hartle has written a contribution to the 23rd Solvay Conference titled Generalizing Quantum Mechanics for Quantum Spacetime. It was delivered there by Murray Gell-Mann and David Gross in the absence of the author (I wonder how many people would have such eminent proxies ;-). The paper is very pedagogically written, starting practically from textbook QM which Hartle developes into a more general form.

"The key idea is that the fine-grained histories do not have to represent evolution in spacetime. Rather they can be histories of spacetime." In a sentence, branch state vectors can be constructed for each coarse-grained history by summing over the metrics and fields in the corresponding class of fine-grained histories. Considerations in signature lead to the conclusion "... if we live in a large universe it must have one time and three space dimensions." Now, if you are not very familiar with Hartle's work it is up to you to read the rest. -- At least try to avoid the two famous bloggers on the right concentrating at the moment in cartoons and movies ... ;-)